Final answer:
By applying the compound interest formula to the investments of Alexx and Spenser, we can calculate the different future values after 30 years considering their respective interest rates, and then compare the results to find the difference.
Step-by-step explanation:
Comparison of Investment Gains Over 30 Years
To compare the future value of investments for Alexx and Spenser, we use the formula for compound interest: Future value = Principal * (1 + Interest rate)number of years t. Alexx invests directly, resulting in an interest rate of 5% per year, whereas Spenser's investment through a retirement fund yields a 4.75% return after accounting for the 0.25% administrative fee.
To calculate Alexx’s future value: $5,000 * (1 + 0.05)30.
To calculate Spenser’s future value: $5,000 * (1 + 0.0475)30.
After performing these calculations, we subtract Spenser's future value from Alexx's to determine how much more Alexx will have than Spenser after 30 years.